4 problems

Let $X_0: x_0^8+x_1^8+x_2^8+x_3^8=0$ be the Fermat octic, and let $C_1$ and $C_2$ be respectively a line, namely a complete intersection of type $(1,1)$, and a complete intersectio…

Let $\overline{\mathcal M}_{g,1}(\pi,d)$ be the moduli space of log-stable maps of degree $d$ to the fibers of the universal family of elliptic curves, with evaluation map…

Let $\mathcal{A}_g$ be the moduli space of principally polarized abelian varieties of dimension $g$. Let…

Let $g=H_Y^2+1\geq 5$ be an odd integer, let $\mathcal F_g$ be the moduli space of polarized $K3$ surfaces of genus $g$, and let $\Sigma_g\subset\mathcal F_g$ be the naturally defi…